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In this paper, we design a variant of the organizational evolutionary algorithm (OEA), called the multipoint organizational evolutionary algorithm (mOEA), for global optimization of multimodal functions. Our objective is to apply crossover strategy of multiple points to enhance the OEA, so that the resulting algorithm can improve the precision of the solutions and have a fast convergence rate. In the mOEA, crossover among many leaders enables the diversity of the leader swarm to be preserved to discourage premature convergence. Another new organizational operator, the integrating operation replacing Annexing manipulation, guarantees members of each organization to converge to the leader fast and also have a good diversity due to mutation. Experiments on six complex optimization benchmark functions with 30 or 100 dimensions and very large numbers of local minima show that, comparing with the original OEA and CLPSO, mOEA effectively converges faster, results in better optima, is more robust.